Optimal control of production and maintenance: A cost-efficient approach through inventory and preventive strategies

Messaoud Bounkhel; Lotfi Tadj; Messaoud Bounkhel; Lotfi Tadj

doi:10.3934/era.2025015

Electronic Research Archive

2025, Volume 33, Issue 1: 277-293. doi: 10.3934/era.2025015

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Optimal control of production and maintenance: A cost-efficient approach through inventory and preventive strategies

Messaoud Bounkhel ^{1
,
,},
Lotfi Tadj ²

1.
Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia
2.
Department of Industrial Engineering, Alfaisal University, Riyadh 12714, Saudi Arabia

Received: 03 November 2024 Revised: 06 January 2025 Accepted: 14 January 2025 Published: 22 January 2025

Using an optimal control framework, the optimization of production and maintenance processes is investigated in this paper. We focused on analyzing system behavior, managing costs, and controlling quality. Differential equations are utilized to model the relationship between inventory level, production, and maintenance strategies. A cost function is built combining different cost elements, and the optimal production and maintenance rates were obtained. A sensitivity analysis is performed to assess the impact of different parameters on the total cost and on the optimal solution. The key findings demonstrated that higher initial inventory levels significantly decreased long-term costs and improved production efficiency. The optimal preventive maintenance strategy emphasized the importance of early investments in quality and maintenance, leading to sustained operational stability.
- inventory,
- deterioration,
- optimal control,
- production,
- maintenance,
- obsolescence
Citation: Messaoud Bounkhel, Lotfi Tadj. Optimal control of production and maintenance: A cost-efficient approach through inventory and preventive strategies[J]. Electronic Research Archive, 2025, 33(1): 277-293. doi: 10.3934/era.2025015

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Abstract

Using an optimal control framework, the optimization of production and maintenance processes is investigated in this paper. We focused on analyzing system behavior, managing costs, and controlling quality. Differential equations are utilized to model the relationship between inventory level, production, and maintenance strategies. A cost function is built combining different cost elements, and the optimal production and maintenance rates were obtained. A sensitivity analysis is performed to assess the impact of different parameters on the total cost and on the optimal solution. The key findings demonstrated that higher initial inventory levels significantly decreased long-term costs and improved production efficiency. The optimal preventive maintenance strategy emphasized the importance of early investments in quality and maintenance, leading to sustained operational stability.

References

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